6533b872fe1ef96bd12d378b

RESEARCH PRODUCT

p-Parts of Brauer character degrees

Gabriel NavarroPham Huu TiepHung P. Tong-viet

subject

CombinatoricsFinite groupAlgebra and Number TheoryCharacter (mathematics)Brauer's theorem on induced charactersSolvable groupStructure (category theory)Mathematics::Representation TheoryPrime (order theory)Mathematics

description

Abstract Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

yearjournalcountryeditionlanguage
2014-02-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2014.01.022